Page 246 - DMTH201_Basic Mathematics-1

Unit 8: Continuity

First we examine continuity at x = 50 Notes
LHL = 30 × 50 = 1500
RHL = 29 × 50 = 1450.

Since LHL RHL, the function is discontinous at = 50.
At other values of the function is a polynomial which is continuous.

8.5 Summary

Every polynomial function is continuous at every real number.
Every rational function is continuous at every real number in its domain.
Every exponential function is continuous at every real number.

Every logarithmi-c function is continuous at every positive real number.
f(x) = sin x and g(x) = cos x are continuous at every real number.
h(x) = tan x is continuous at every real number in its domain.
A function f is continuous from the right at x = a provided that

A function f is continuous from the right at x = b provided that
Let f (x) be a continuous function on the interval [a, b]. If d [f (a), f (b)], then there is a c
[a, b] such that f (c) = d.

8.6 Keywords

Continuity on an Interval: A function f is said to be continuous on an open interval (a, b) provided
that f is continuous at every value in the interval.

Infinite Limits: The sign of the infinite limit is determined by the sign of the quotient of the

numerator and the denominator at values close to the number that the independent variable is
approaching.
8.7 Self Assessment

1. If f(x) = Ax – 4 of 1 4 then value of f(x) is

(a) A – 2
(b) A + 2
(c) A – 4
(d) A + 4

2. find value of when
(a) 0
(b) –
(c)
(d) 1

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